Determine position of scattered events in pixelated gamma detector using inverse energy weighting

Abstract

A method and apparatus are provided for positron emission imaging to correct a position at which a gamma ray was detected, when the gamma ray is scattered during detection. When Compton scattering occurs during detection of a gamma ray, the energy of the gamma ray deposited in multiple crystals in an array of detector elements. The corrected position is determined as a weighted sum of the position of the multiple crystals, each weighted by an inverse of the energy measured at the respective crystal. Further, the inverse-energy weight can be raised to a power p. A minimum energy threshold can be applied to determine the multiple crystals at which the gamma ray energy is deposited. The corrected position can be a floating position or can be rounded to a nearest crystal or to a nearest virtual sub-crystal.

The invention claimed is: 
     
       1. A positron emission imaging apparatus, comprising:
 processing circuitry configured to
 obtain emission data representing positions and energies of gamma rays incident at a plurality of detector elements, each detector element of the plurality of detector elements including a respective photodetector and scintillator crystal, the scintillator crystal of the each detector element being, at least partially, isolated from other scintillator crystals of the plurality of detector elements, 
 correct an incident position of a primary gamma ray, when the primary gamma ray is scattered, using an inverse-energy weighting to combine a position of the primary gamma ray with a position of a corresponding scattered gamma ray to generate a corrected position, wherein the inverse-energy weighting divides a respective position of the emission data by a corresponding energy of the emission data that have been raised to a power p, wherein p is a positive number, and 
 reconstruct an image using the emission data together with the corrected position. 
 
 
     
     
       2. The apparatus according to  claim 1 , wherein the processing circuitry is further configured to correct the incident position by sub-dividing a cross-sectional area of a closest scintillator crystal of the plurality of detector elements, which is closest to the corrected position, into virtual sub-crystals, and identifying the corrected position as being at one of the sub-crystals for which a distance measure to the corrected position is smallest. 
     
     
       3. The apparatus according to  claim 2 , wherein the processing circuitry is further configured to correct the incident position, wherein the identifying the corrected position as being at the one of the sub-crystals is performed using the distance measure that is a Euclidean distance from a respective center of a virtual sub-crystal to the corrected position. 
     
     
       4. The apparatus according to  claim 1 , wherein the processing circuitry is further configured to correct the incident position by
 applying an energy threshold to the energies the plurality of detector elements that occur within a detection time window, and determining that the scattered gamma ray was detected when two or more of the energies detected within the detection time window exceed the energy threshold, and 
 the combination of crystal positions for the corrected position is calculated by summing applying the inverse-energy weighting to crystal positions of detector elements corresponding to the energies exceeding the energy threshold to generate weighted crystal positions and then summing the weighted crystal positions. 
 
     
     
       5. The apparatus according to  claim 1 , wherein the processing circuitry is further configured to correct the incident position, wherein p is an integer in a range from 0 to 10. 
     
     
       6. The apparatus according to  claim 1 , wherein the processing circuitry is further configured to correct the incident position, wherein the corrected position is a floating position that is independent of a crystal grid of the plurality of detector elements. 
     
     
       7. The apparatus according to  claim 2 , wherein the processing circuitry is further configured to correct the incident position by applying a sub-division criterion to determine whether to sub-divide the closest scintillator crystal into the virtual sub-crystals. 
     
     
       8. The apparatus according to  claim 2 , wherein the processing circuitry is further configured to correct the incident position, wherein the sub-division criterion is that the closest scintillator crystal is sub-divided in to the virtual sub-crystals when, for the emission data, a count of corrected positions for the closest scintillator crystal exceeds a count threshold. 
     
     
       9. The apparatus according to  claim 2 , wherein the processing circuitry is further configured to correct the incident position, wherein the closest scintillator crystal is sub-divided into more virtual sub-crystals when the primary gamma ray results in a single scattered gamma ray than when the primary gamma ray results in multiple scattered gamma rays. 
     
     
       10. The apparatus according to  claim 4 , wherein the processing circuitry is further configured to
 calibrate, using calibration data, an optimal value for the energy threshold and an optimal value for the power p, which is used to calculate the inverse energy weights. 
 
     
     
       11. A positron emission imaging method, comprising:
 obtaining emission data representing positions and energies of gamma rays incident at a plurality of detector elements, each detector element of the plurality of detector elements including a respective photodetector and scintillator crystal, the scintillator crystal of the each detector element being, at least partially, isolated from other scintillator crystals of the plurality of detector elements, 
 correcting an incident position of a primary gamma ray, when the primary gamma ray is scattered, using an inverse-energy weighting to combine a position of the primary gamma ray with a position of a corresponding scattered gamma ray to generate a corrected position, wherein the inverse-energy weighting divides a respective position of the emission data by a corresponding energy of the emission data that have been raised to a power p, wherein p is a positive number, and 
 reconstructing an image using the emission data together with the corrected position. 
 
     
     
       12. The method according to  claim 11 , wherein the correcting of the incident position is performed by sub-dividing a cross-sectional area of a closest scintillator crystal of the plurality of detector elements, which is closest to the corrected position, into virtual sub-crystals, and identifying the corrected position as being at one of the sub-crystals for which a distance measure to the corrected position is smallest. 
     
     
       13. The method according to  claim 12 , wherein the correcting of the incident position includes that the identifying the corrected position as being at the one of the sub-crystals is performed using the distance measure that is a Euclidean distance from a respective center of a virtual sub-crystal to the corrected position. 
     
     
       14. The method according to  claim 11 , wherein the correcting of the incident position is performed by
 applying an energy threshold to the energies the plurality of detector elements that occur within a detection time window, and determining that the scattered gamma ray was detected when two or more of the energies detected within the detection time window exceed the energy threshold, and 
 the combination of crystal positions for the corrected position is calculated by summing applying the inverse-energy weighting to crystal positions of detector elements corresponding to the energies exceeding the energy threshold to generate weighted crystal positions and then summing the weighted crystal positions. 
 
     
     
       15. The method according to  claim 11 , wherein the correcting of the incident position includes that the corrected position is a floating position that is independent of a crystal grid of the plurality of detector elements. 
     
     
       16. The method according to  claim 11 , wherein the correcting of the incident position includes that the power p, which is used in the inverse-energy weighting, is an integer in a range from 0 to 10. 
     
     
       17. The method according to  claim 12 , wherein the correcting of the incident position is performed by applying a sub-division criterion to determine to sub-divide the closest scintillator crystal into the virtual sub-crystals when, for the emission data, a count of corrected positions for the closest scintillator crystal exceeds a count threshold. 
     
     
       18. The method according to  claim 12 , wherein the correcting of the incident position includes that the closest scintillator crystal is sub-divided into more virtual sub-crystals when the primary gamma ray results in a single scattered gamma ray than when the primary gamma ray results in multiple scattered gamma rays. 
     
     
       19. The method according to  claim 14 , further comprising:
 calibrating, using calibration data, an optimal value for the energy threshold and an optimal value for the power p, which is used to calculate the inverse energy weights. 
 
     
     
       20. A non-transitory computer readable storage medium including executable instructions, wherein the instructions, when executed by circuitry, cause the circuitry to perform the method according to  claim 11 .